Generation of weakly damped electron plasma surface waves on a semiconductor: amplification and coupling of acoustic waves on an adjacent piezoelectric

ABSTRACT

Conduction electrons in a semiconductor which is subjected to an applied electric drift field and magnetic field are excited to give rise to a weakly damped electron plasma surface wave carrying negative or positive energy depending upon the direction of the applied magnetic field. Acoustic waves traveling along the surface of an adjacent piezoelectric are resonantly amplified and coupled to the electron surface waves.

United States Patent 1 [111 333mm Bers 1 May 1, 1973 [54] GENERATION OF WEAKLY DAMPED [58] Field of Search ..330/5.5

ELECTRON PLASMA SURFACE WAVES ON A SEMICONDUCTOR: AMPLIFICATION AND COUPLING OF ACOUSTIC WAVES ON AN ADJACENT PIEZOELECTRIC Inventor: Abraham Bers, Arlington, Mass.

Assignee: Massachusetts Institute of Technology, Cambridge, Mass.

Filed: Apr. 16, 1971 Appl. N0.: 134,854

Primary ExaminerRoy Lake Assistant Examiner-Darwin R. Hostetter Att0rneyThomas Cooch et al.

57 ABSTRACT Conduction electrons in a semiconductor which is subjected to an applied electric drift field and magnetic field are excited to give rise to a weakly damped electron plasma surface wave carrying negative or positive energy depending upon the direction of the applied magnetic field. Acoustic waves traveling along the surface of an adjacent piezoelectric are resonantly amplified and coupled to the electron surface waves.

7 Claims, 21 Drawing Figures SEMICONDUCTOR SlGNAL OUT PIEZOELECTRIC l PATENTEDHAY Hm 3151.214

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ABRAHAM B595 ATTORNEY PAT ENTED 1 AMPLfFICATION (dB /cm) AMPLIFICATION (dB lcrn) mm 5 OF 9 Bus) 50 p Ems) O L l 1 1 1 DRIFT HELD (V/cm) F IG 5B Ir-WLMTQR:

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INVENTOR ABRAHAM eERs ATTORNE Y GENERATION OF WEAKLY DAMPEI) ELECTRON PLASMA SURFACE WAVES ON A SEMICONDUCTOR: AMPLIFICATION AND COUPLING OF ACOUSTIC WAVES ON AN ADJACENT PIEZOELECTRIC FIELD OF INVENTION This invention relates generally to ultrasonics and semiconductor technology.

PRIOR ART Surface acoustic waves traveling on a piezoelectric have been amplified by their non-resonant interaction with drifting electrons in an adjacent semiconductor. The mechanism of amplification, as in the well-known bulk amplifier, is basically a non-resonant coupling of the acoustic wave to the electrons. For example, the principle of coupling to the drifting carriers from a slow TM wave 'carried by an electromagnetic circuit is described by M. Sumi, Japan, J. Appl. Phys. 6, 688 (1967). The principle of coupling across the finite gap between a piezoelectric crystal and an adjacent semiconductor is reported by J. H. Collins et al., App. Phys. Letters 13, 314 (1968).

In this process, the electron system presents a smallsignal negative-real conductivity when its drift velocity v, exceeds the sound velocity of the acoustic wave to be amplified, v,,. If the carriers travel in the same direction as the surface waves, the wave is amplified, but the wave is entirely established by the acoustic system. The mechanism involved is non-resonant coupling between the acoustic wave and the electrons. The consequence of this is that amplification occurs over a broad frequency range with a frequency of maximum growth independent of v,,, and with growth rates and amplified bandwidth proportional to the square of the effective electromechanical coupling constant.

SUMMARY OF INVENTION 1. In view of the aforesaid art, it is one object of applicants invention to generate a weakly damped electron plasma surface wave on a semiconductor.

2. It is another object of the invention to amplify and/or couple acoustic waves on a piezoelectric to a weakly damped electron plasma surface wave on an adjacent semiconductor wherein the frequency of maximum growth rate is tunable with the drift velocity and wherein the amplified bandwidth and maximum growth rate are proportional to the electromechanical coupling constant.

3. It is another object of the invention to excite and generate a weakly damped electron plasma surface wave on a semiconductor which, in turn, is transduced to an acoustic wave on an overlapping piezoelectric.

4. It is another object of the invention to couple and transduce acoustic waves on a piezoelectric to electric signals on an overlapping semiconductor.

5. It is another object of the invention to attenuate acoustic waves on a piezoelectric by controlling the magnitude of an electric drift field and a transverse magnetic field applied to an adjacent semiconductor on I which there is a highly damped surface wave.

6. It is another object of the invention to enhance the excitation of acoustic waves by interdigital finger transducers on a piezoelectric surface.

These and other objects are principally met by a semiconductor with means of applying an electric drift field and means of applying a transverse magnetic field.

If an acoustic wave is generated on an adjacent piezoelectric crystal, a weakly damped electron plasma surface wave will be excited on the semiconductor which interacts resonantly with the acoustic wave. The coupled wave has a frequency of maximum growth rate tunable by v,,; and a maximum growth and an amplified bandwidth proportional to the electromechanical coupling constant K. Under these conditions there is resonant amplification of the acoustic wave.

Under the same conditions, reversing the direction of the magnetic field converts the system to an almost loss-free tunable coupler by which there is a complete transfer of signal energy from the electron surface wave to the acoustic surface wave.

A weakly damped electron plasma surface wave may be excited on the semiconductor surface by an electrical signal and transduced to an acoustic signal on an overlapping piezoelectric or the reverse process may take place. The combined processes can take place on a piezoelectric semiconductor excited by an electric signal.

Critical to these processes is the propagating of a weakly damped plasma wave on the semiconductor surface. This is the essence of applicants invention.

Further objects and a better understanding of the apparatus thereof will become more apparent with the following description taken in conjunction with the following drawings:

FIG. 1 Block diagram of adjacent semiconductorpiezoelectric apparatus.

FIG. 1A Detailed view of surface areas.

FIG. 2 Dispersion diagram illustrating amplification mode.

FIG. 3A Normalized growth rate of acoustic surface wave as a function of the ratio of electron drift velocity to acoustic surface wave velocity.

FIG. 3B Normalized growth rate of acoustic surface wave as a function of the ratio of electron drift velocity to acoustic surface wave velocity with diffusion effects taken into consideration.

FIG. 4A Normalized growth rate of acoustic surface wave as a function of the ratio of the acoustic wave frequency to the relaxation frequency.

FIG. 4B Normalized growth rate of acoustic surface wave as a function of the ratio of the acoustic wave frequency to the relaxation frequency with diffusion effects taken into consideration.

FIG. 5A Experimental amplification of acoustic surface waves as a function of electric drift and magnetic fields.

FIG. 5B Theoretical amplification of acoustic surface waves as a function of electric drift and magnetic fields.

FIG. 6 Dispersion diagram illustrating passive mode coupling.

FIG. 7A Acoustic surface-wave coupling as a function of electric drift field for 30 MHz frequency.

FIG. 8B Acoustic surface wave attenuation as a function of magnetic field with no applied drift field for 150 MHz frequency.

FIG. 9 ldealized dispersion diagram with no applied electric drift field.

FIG. 10 Theoretical amplification of acoustic surface waves as a function of the ratio of the acoustic wave frequency to the relaxation frequency for various semiconductor thicknesses.

FIG. 11 Theoretical amplification of acoustic surface waves as a function of the ratio of the acoustic wave frequency to the relaxation frequency for various semiconductor thicknesses with diffusion taken into consideration.

FIG. 12 Block diagram of overlapping piezoelectric semiconductor apparatus transduxing acoustic to electron wave signals.

FIG. 13 Schematic of power flow characteristics of the acoustic and electron surface waves within the overlap region of apparatus illustrated in FIG. 12.

FIG. 14 Block diagram of overlapping piezoelectric-semiconductor apparatus transducing electron .wave signals to acoustic signals.

FIG. 15 Block diagram of piezoelectric-semiconductor apparatus.

PREFERRED EMBODIMENT The essence of applicant's invention is that a weakly damped surface plasma wave can be generated on a semiconductor subjected to an electric drift field and an applied magnetic field E where 3,, 1, being the electron mobility of the semiconductor, and where the direction of B is transverse to the velocity of the drift carriers. The carriers may be positive charged holes or electrons. For simplicity, we will deal with electrons, but the teachings infra apply equally to any charged carrier.

A manifestation of applicants invention is illustrated by the apparatus in FIG. 1. A piezoelectric crystal 1, e.g., lithium niobate is placed adjacent to a semiconductor 3, e.g., gallium arsenide. Acoustic surface waves are generated by an electric signal and a pair of interdigital transducers at one end of the piezoelectric crystal 1. They travel'along the surface of the singlecrystal LiNbO 1 and are detected and transduced to electrical signals by a second pair of interdigital transducers 7 at the opposing end of the crystal.

An applied electric drift field is impressed on the semiconductor 3 by applying a voltage, whose polarity is defined as positive in FIG. 1, to two ohmic contacts 8 on opposing ends of the semiconductor. An applied magnetic field E is also applied transversely across the semiconductor 3 and is defined in a positive sense in the direction as shown in FIG. 1.

FIG. 1A shows a detailed view of the region between the semiconductor 3 and piezoelectric l. The air gap, d, is defined as the distance between the semiconductor 3 and piezoelectric 1. The velocity of propagation of the drift electrons, v,,, and acoustic wave, v is defined as positive from left to right as illustrated by the arrows. The extent of the depletion region in semiconductor 3 is illustrated by dashed line 9.

In this situation, the acoustic wave on the surface of the piezoelectric distorts the crystal 1 which gives rise to changing electric fields which, in turn, excite a weakly damped plasma surface wave on the semiconductor 3. This plasma wave couples to the acoustic wave. To see this theoretically, we assume a weak piezoelectric on which a surface wave exp j (wt-k1) propagates in the z direction, 1 being defined as positive from left to right in FIG. 1A. For simplicity we shall ignore the depletion depth d, shown by line 9 in FIG. 1A.

The effective permittivity for the piezoelectric is represented by where a is the permittivity in the absence of piezoelectricity; Av/v is the fractional change in the surface wave velocity when a shorting plane is placed close to, but not in mechanical contact with, the piezoelectric; k,,, is the wave number of the free acoustic surface wave in k(,;(l +Av/v) is the wave number when the electric field outside the piezoelectric is shorted out; and so is the outside the piezoelectric is shorted out; and s is the permittivity in the gap. The semiconductor will be characterized by a single carrier electron dc conductivity p drift velocity v,, across E and permittivity a We use the small-signal, local equations that describe the surface wave on the semiconductor in the absence of diffusion. Assuming that the wave fields are electrostatic, E V, the potentials in three regions of space are required to satisfy the continuity of E and D u at y 1*: d/2, with proper account for the surface current at y d/2. The resultant dispersion relations are:

Eq.] where Av 0( 0 u n I: f v Ep+ O O 2 k =wlv (Raj/v0) -j) q- 3 where v, the drift velocity of the electrons, in 0 o',,/e,( 1+b), and b E uB For a given air gap separation d, k,, is the propagation constant of the acoustic surface wave when 0,, O and k is the propagation constant of the electron surface wave when Av/v 0.

The dispersion relation, Eq. 1 represents the coupling of these waves, the righthand .side being the coupling coefficient which is a slowly varying function of k, and proportional to an effective electromechanical coupling constant (Av/v)G 5 K Assuming that the acoustic surface wave is essentially undamped, Eq. 1 may exhibit two distinct types of interactions depending upon the damping rate of the electron surface wave,

which is given by k the imaginary part of k as defined by Eq. 3. If {bI I, then one can see from Eq. 3 that k k k being the real part of k,,. Under where K (GAv/v) the effective electromechanical coupling constant, and Q= R to o'*bk,,,. When B is positive as defined in FIG. 1, b is positive and hence the second term under the radical in Eq. 8 is positive.

When k k the first term becomes smaller than the second, and the radical becomes negative, yielding a solution for k,. For values of positive k,, there is amplification, with the frequency of maximum growth rate k, occuring when k, k, and being tunable with v,,. The maximum growth rate and the amplified bandwidth are proportional to the square root of [GO/2v, and hence proportional to the effective electromechanical coupling constant K (Av/v)G. This is a strong resonant condition. When k k and k K /2v,,, there exists a weakly resonant condition.

The solutions for strong resonance, i.e., k K n/2w, are illustrated graphically in FIG. 2. This is a plot of k versus (0,, the real part of w. The light lines 9 and 11 illustrate the uncoupled electron and acoustic waves respectively. The slope of line 11 is simply v,, /k,,. The slope of line 9 is v,,, and its and k intercepts are |b|Rm,,* and RwflIbl/v0 respectively as is readily seen from Eq. 3 by setting to 0 and then k 0. The bold lines in FIG. 2 represent solutions for k in Eq. 1. The imaginary part of the solutions, k,, is shown in dashed lines. When k, is positive, amplification takes place. The frequency of maximum growth rate k, occurs when k,, k,, the first term under the radical in Eq. 8 going to zero. From Eq. 3- we also see that when ka ke, v0=v,1[l+Rw/bw]. Hence, since b is positive, v,, v,,. Additionally, the weakly damped electron wave has a negative small-signal energy which is represented by a6 sign next to line 9 and the acoustic wave is in a positive energy mode which is represented by as; sign next to line 11. Under these conditions there is atransfer of energy from the electron wave to the acoustic-wave whereby amplification takes place. The interaction here is of:a resonant wave-wave type as contrasted with non-resonant coupling between the acoustic wave and the drift electronS in the absence of a magnetic field B,,.

In order to get maximum coupling and gain, the semiconductor 3 should be as close as possible to piezoelectric l but not in mechanical contact with it. The separation distance d must be small compared to the acoustic wave length. If, however, a broader bandwidth is important, d may be increased, but maximum coupling and gain must be sacrificed.

The above dispersion relations do not take into consideration electron diffusion effects which reduce the interaction. If diffusion is considered, then the smallsignal electric potential inside the semiconductor must now be modified to include a part that derives from the bulk charge density, and the boundary condition of a surface current at y d/2 is replaced by the vanishing of the normal component of the current. The resultant dispersion relation including-the effects of diffusion and a depletion region, but ignoring the gap, is:

k, is the wave number of the electron surface wave when (Av/v), is zero, (Av/v), being the fractional change in the acoustic phase velocity when 0', changes from infinity to zero. (Av/v), is related to (Av/v) by the equation: (Av/v) =[(e,,+e0)/(eDe,)](Av/v). is the effective dielectric relaxation frequency as defined above. is the effective electron diffusion frequency in the magnetic field and is equal to (m/k) (l+b )e/kTu, T being the electron temperature and k being Boltzmanns constant. e, and e, are the dielectric constants for the piezoelectric and semiconductor respectively. The factor R represents a reduction in the effective electron conductivity for the interaction arising from the geometry and the differences in dielectric constants. The effective electromechanical coupling constant K is similarly affected and thus becomes frequency-dependent. The factor Q arises from the effects of electron diffusion due to their finite temperature. d is the depletion depth, the distance between the surface of the semiconductor 3 and line 9. In deriving Eqs. 9 12, the air gap d between piezoelectric 1 and semiconductor 3 is assumed negligible compared to the depletion depth d In this connection it should be noted that the weakly damped plasma wave has been I described as a surface wave. Where there is a finite depletion depth, it is more accurate to describe the propagating surface of this wave at the depletion depth 9 illustrated in FIG. 1A. Similarly, as can be seen from Eqs. 9 11, the smaller the depletion depth, the larger the coupling. In a particular semiconductor the deple-. tion depth may be effectively decreased-by applying a voltage across the semiconductor 3 and piezoelectric 1 in accordance with standard techniques.

By comparing Eqs. 1 7 with Eqs. 9 13, one can see the effects of diffusion. From Eq. 9 it is observed that for diffusion to have minimal effects, Q as defined by Eq. 13 must be much smaller than one. This imposes the condition:

where 1 equals (v,,/v,,)-l (kv,,/m)l. c

The interaction frequency is determined by Eq. 3. If b I, and k, is set equal to k m/v then w z Ram/b1 where 0),, is equal to mile, the dielectric relaxation frequency. Correspondingly, if we let (0,, be the electron diffusion frequency equal to (w/kPe/kTp, where k is Boltzmann's constant, T is the electron temperature and e is the charge of an electron, then the above condition for negligible damping due to diffusion becomes:

When the magnetic field is reversed, v, v,, and we find:

In the absence of a magnetic field, electron waves in semiconductors are well known to be heavily damped. This comes about because of the high electron-lattice collision frequency (which at best is one to two orders of magnitude higher than microwave frequencies) and thermal diffusion, both effects leading to a rapid debunching of the electrons associated with a coherent wave. When a strong magnetic field, [bl 1, is applied transverse to the direction of wave propagation which is also the direction of electron bunching) the debunching due to thermal diffusion is reduced. The conditions for a weakly damped surface wave are:

where e is the magnitude of the applied electron field and n is the number of drift electrons, and D is the diffusion constant.

FIGS. 3A and 3B illustrate some of the above considerations. In FIG. 3A, the growth rate of the acoustic surface wave k, normalized to the free acoustic wave number k is plotted versus the ratio of the electron drift velocity, v,,, to the acoustic surface wave velocity v,, for various values of b p.8 B, is taken in the sense shown in FIGS. 1 and 1A. Additionally, K =0.01, R0) lon 50, with R =0.2 and m U /m= 250. is broad and reflects non-resonant interaction. As 3,, and hence b, is increased, the curves become narrower, indicating amplification over a narrow range of values for v lv i.e., resonant amplification. FIG'. 33 illustrates the effects of diffusion. Here m lw 250. The curves are all substantially broader and amplification is decreased.The effects of diffusion may decrease the maximum am plification as b is increased. In particular, at b 25, there is a substantial decrease in amplification.

FIGS. 4A and 4B, the normalized growth rate k,/k,,, is plotted versus, the ratio of the acoustic wave frequency to the relaxation frequency w for K =0.0l, R =02, v lv, S, and m lm 0. For higher values of b, we have resonant amplification. In FIG. 43,0; 6 In) 250, and the electron diffusion effects cause broadened curves and decreased amplification. Resonance occurs at lower frequencies. This also can be seen from FIG. 2. Line 9 represents the plot of k versus a), for the carrier wave without diffusion effects in the uncoupled mode. This is in effect the graph of Eq. 3. With diffusion, we must look at Eq. 10 from which it is seen that line 9 must be shifted .to the left and hence its intersection with line 1 1 is at a lower frequency.

FIGS. A and 5B are, respectively, graphs of the theoretical and experimental amplification expressed in decibels per centimeter for magnetic fields B, of dif ferent magnitudes. The experimental curves represent data taken using a GaAs semiconductor 1 with electron drift mobility p, 5000cm V"S", free carrier density n 1.3 X l0 cm' and a depletion-region depth, 11 2.1 X 4 cm. The GaAs crystal was 8 mm in the zdirection, 0.3 mm thick in the y-direction, and 3 mm in width with its surface optically polished by using chemical-mechanical polishing procedures. The ohmic contacts 8 were placed along the 3 mm edge. The

piezoelectric 3 was LiNbO with the acoustic waves propagating along the positive 1 direction as defined in FIG. LA, on a Y-cut polished surface. The acoustic waves were generated by a pair of interdigital transducers 5 of MHZ fundamental frequency. The interaction length, the region over which the GaAs and LiNbO are in close proximity, was 5 mm. The air gap in the interaction length was less than 1000 Angstroms. The experimental curves in FIG. 5A qualitatively confirm the predicted theoretical results shown in FIG. 5B. For instance, for zero magnetic field, there is a very broad curve indicating non-resonant interaction. For increasing values of B the curves become narrower and amplification is enhanced. This is in agreement with Eq. 8 which shows that k, increases as B, increases. At the highest magnetic field, there is some decrease in amplification due to electron diffusion effects.

The relative shift of the peaks in amplification to lower drift voltages for increasing magnetic fields is also in agreement with the theory. This can be seen from FIG. 2. The to, intercept is Rm* |b| Since a) m /l+b then for large values of b, the w, intercept is proportional to Rw lb. As B, is increased, the w,- intercept becomes smaller. If now line 9 is to intersect line 11 at the same point, i.e., to, remaining constant, the k intercept must decrease, and correspondingly, the slope which is equal to v, must decrease. The drift velocity v, is equal to ,u. times the applied electric field. Hence, the relative shift of peaks to lower-drift voltages at the same frequency for increasing magnetic fields.

Although there is qualitative agreement between the results and the theory, the experimental curves do show peaks at somewhat higher drift fields, broader resonances, and considerably less gain than the theoretical curves. These differences result from resistivity inhomogeneities which are known to exist in GaAs and additionally from electron trapping.

If the polarity of B, is reversed, i.e., opposite to what is depicted in FIG. 1A, the apparatus in FIG. 1 becomes an almost loss-free tunable coupler instead of an amplifier. This can be seen from Eq. 8. The term K Q./2v must be positive as b is negative. Hence, the radical is positive and there is no solution for k, leading to amplification. This is shown graphically in FIG. 6. The uncoupled positive energy mode of the acoustic wave remains unchanged from that shown in FIG. 2. It is shown by light line 11. The mode is now positive, however, and is shown by light line 14. Its m intercept is Rw 1b| /v,, due to the sign change in b in Eq. 3. From Eq. 8 it can be seen that the strongest interaction takes place when k, k r and decreases as (k -It increases from zero. The coupling is tunable with v,,. Additionally from Eq. 3, v, v,,(lm U R/bm), and hence v, v,,. Both waves are in the positive energy mode which is indicated by the symbolggplaced next to lines 1 1 and 14.

In FIGS. 7A and 7B, attenuation of the acoustic sur face wave in decibels per centimeter is plotted versus drift field in volts per centimeter for 30 MHz and 150 MHz signals respectively. These curves are the experimental data taken from an apparatus described above, but with a magnetic field opposite to that shown in FIG. 1A. Here, ]k k and lie K Q/2v,,. Since the electron surface wave is in a positive energy mode, the acou stic wave transfers energy to it, which results in the attenuation of the acoustic wave.

The experimental curve in FIG. 7A exhibits the magnitude, i.e., 80 dB/cm, and sharpness characteristic of resonant interaction. By contrast, the attenuation at 30 MHz for zero magnetic field is broad and shallow with a maximum loss of 12 dB/cm at a drift field of -700v/cm. The peak of the theoretical curve based on the dispersion relations has a higher peak attenuation at a slightly lower drift field. The difference between the theoretical predictions and the experimental curve is again caused by resistivity inhomogeneities in the GaAs semiconductor and by electron trapping.

It can be seen from FIG. 7B that the maximum attenuation at 150 MHz is substantially lower than that for 30 MHz. This results from electron diffusion effects which reduce the interaction at high frequencies The experimental curve is in close agreement with the theoretical results predicted by the dispersion relations. At this frequency the resistivity inhomogeneities in the semiconductor and the electron trapping effects are not very pronounced.

It should be noted here that the resonant amplification and coupling described above and illustrated in FIGS. 3A, 3B, 7A and 78 take place when the apparatus in FIG. 1 is operated under the condition that b 1 where b B u. As was said above, as a result of this condition, Eq. 3 shows that k k and the carrier surface wave is weakly damped, and the resultant dispersion relation is given by Eq. 8. However, if |b| I or 1b] 1, then Eq. 3 shows that the carrier surface wave is heavily damped, i.e., k k Under these conditions, the interaction between the acoustic wave and carriers is nonresonant. Since the perturbation of the acoustic wave number is small in where 1; (v,,/v,,)l. This equation is precisely in the form of the well-known bulk-wave interaction. The imaginary part gives the growth rate of the acoustic surface wave and is thus seen to be proportional to the real part of the effective small-signal conductivity of the electrons. The growth rate k, is now proportional to G(Av/v)=K and the amplifier bandwidth is entirely determined by the frequency dependence of the carrier small-signal conductivity evaluated at the acoustic phase velocity.

As we have already seen in FIGS. 3A, 38, 41A and 4B, for low values of b having direction shown in FIG. 1A, there exists this type of non-resonant amplification. If the direction of B is opposite to that shown in FIG. 1A and if we now consider low values of b, i.e., b l or b x l, the system becomes dissipative and the apparatus in FIG. 2 functions as an attenuator without coupling in contradistinction to the almost loss-free tunable coupler as is illustrated in FIGS. 7A and 78 where the magnetic field had a magnitude of 140 KG, and consequently |b| I. As a coupler, the energy is transferred to the electron wave instead of being dissipated and the nature of the interaction is wave-wave instead of wave-electron.

Let us now consider the operation of the apparatus in FIG. 1 with zero drift field. When the magnetic field is in the direction shown in FIG. 1A, there is no interaction. This will be shown in FIG. 9 momentarily. If the magnetic field is opposite to that shown in FIG. 1A, we must examine separately the conditions lb] l and lbl 1. When |b| I, it is difficult to describe the exact nature of the interaction. However, as indicated above, the electron wave is highly damped and the apparatus acts essentially as an attenuator without coupling. As b is increased to high values, the interaction partakes more of a wave-wave type and hence acts as an almost loss-free tunable coupler for very high values of 8,. From Eqs. 2 and 3, maximum interaction ignoring diffusion, is when w Rm U Ibl This condition is nearly satisfied at 150 MHZ with B having a magnitude of KG. FIGS. 8A and 8B illustrate these considerations. The curves are plots of attenuation in db per cm versus magnitude of magnetic field with no drift field applied to the semiconductor. FIG. 8A is for a 30 MHz frequency and FIG. 8B is for a MHz frequency. Lines 18 and 20 are plots for when the magnetic field is applied in the direction shown in FIG. 1A, i.e., no interaction. Lines 17 and 19 are plots when the magnetic field is applied in an opposite direction to the one shown in FIG. 1A. As predicted, the attenuation is substantially higher at higher frequencies.

These considerations are illustrated more clearly by the dispersion diagram in FIG. 9. The acoustic wave is again represented by line 11. Since v, is now zero, the slope of line 11 in FIG. 2 now becomes zero, i.e., it is horizontal and represented by line 15 in FIG. 9. For high values of B and direction opposite that shown in FIG. 1A, the condition is satisfied that (u z Rm 0 [bl and hence interaction. However, when 8,, is in the direction as shown in FIG. 1A, a) z Rw, |b| as is represented by line 16. Clearly, there is no interaction as was alluded to above.

Up to this junction we have not considered the thickness of semiconductor 3. All the above graphs and equations hold for thicknesses T which are much greater than w /v =q These considerations are illustrated in FIGS. 10 and 11. In FIG. 10 we neglect diffusion, take K =0.0l, R =0.2 and v /v, 5 and b 10, with the direction of B the same as illustrated in FIG. 1A. The growth rate of the acoustic surface wave k, normalized to the free acoustic wave number k is plotted versus the ratio of the acoustic wave frequency to the relaxation frequency. For q r l, we have a broad curve. As this is increased, the curves become narrower and resonant amplification is seen. FIG. Ill illustrates the effects of taking diffusion into consideration. Here we take the same parameters as in FIG. 10, but m /w,, 100. The curves are for q 7' equal to the same values as in FIG. 10, but with q,, equal to one-tenth q (1,, is equal to l/A where A is the Debye wavelength. Qualitatively, the curves are broader with some decrease in amplification.

Thin film semiconductors are sometimes desirable for spacial requirements and thermal considerations. Hence, the constraint A T is of practical importance.

The apparatus illustrated in FIG. 1 is just one manifestation of the invention, that is the subjecting of a semiconductor to applied electric and transverse magnetic fields. All the above teachings can be manifested in different apparatus. For instance, one

can use a semiconductor by itself. In this case an electrical signal is applied to the surface of the semiconductor by standard techniques, e.g., M.O.S. If the semiconductor is subjected to an electric drift field and a magnetic field where lb] 1, b p8,, and nkTle E 1, a weakly damped surface wave will be generated on the surface. If 8,, is in the direction shown in FIG. 1A, the energy will flow from the signal source, and in the opposite direction into the signal source. The signal may be tapped off the opposing end.

FIG. 12 illustrates another example embodying the above principles, an electro-acoustic transducer. An electrical signal is fed into piezoelectric 18 and an acoustic surface wave is generated by interdigital trans ducers 19. The surface wave travels along the piezoelectric while being very slightly damped. In the region of overlap between the semiconductor 20 and piezoelectric 18, the acoustic wave excites a weakly damped plasma wave on the semiconductor. This is caused by the changing electric fields inherent in the piezoelectric caused by the stress on the piezoelectric by the acoustic wave. The acoustic wave will be coupled to the semiconductor for the direction of the magnetic field as shown in FIG. 12. If the field is reversed, amplification will also take place over the interlap region. The output signal is tapped by MOS 21. Hence, the acoustic signal has been transduced to an electrical signal. Such a device is useful as a delay line. The input signal is converted to acoustic signals which have a relatively slow velocity, and then reconverted after amplification and delay, back to electrical signals.

In order to determine the minimum distance over which the semiconductor 3 and piezoelectric 1 must be overlapped in order to transfer the energy of the acoustic wave to a weakly damped carrier wave, we must examine Eq. 8. Taking k k k the solution to Eq. 14 exhibits two waves, both propagating in the z-direction as defined in FIGS. 1A

and FIG. 12;

k k,,, C Eq. 17

If we assume 2 0, at the beginning of the region of overlap, see FIG. 12, and the amplitude of the acoustic wave potential isA and zero for the electron wave, then the amplitudes for the acoustic and electron waves will be for z min l imar m imar q- 20 Examining FIG. 4A, we find typically z /it 10.

FIG. 13 illustrates the amplitudes of the acoustic and electron waves in a region of minimum overlap. As the amplitude of the acoustic wave decreases, the amplitude of the electron wave increases correspondingly, with a complete transfer in the distance 1r/2C. Hence in order to achieve complete transfer, the overlap distance must be a multiple of the coupling wavelength, IT/2C.

The minimum interaction length for complete transfer of energy is again 1r/2C with the amplitude of the electron wave decreasing and the amplitude of the acoustic increasing correspondingly.

Another useful result of overlapping is the enhancement of the acoustic excitation on a piezoelectric by interdigital finger transducers. If a semiconductor overlaps that section of the piezoelectric wherein lay the interdigital transducer, the acoustic wave excitation will be enhanced by subjecting the semiconductor to applied electric' and transverse magnetic fields in accordance with the above teachings.

FIG. 15 illustrates the use of a piezoelectric-semiconductor 30. Here an electrical signal is converted to an acoustic signal which is amplified on the surface with the direction of the magnetic field shown. A further variation would consist in using a crystal which has semiconductor properties on one end and piezoelectric on an opposing end.

What is claimed is:

1. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal comprising:

a. a semiconductor located immediately adjacent to and with a surface substantially parallel to said piezoelectric surface,

b. means for applying a drift field across and parallel to the surface of said semiconductor adjacent to said piezoelectric, with a direction opposing the direction of propagation of said acoustic wave and of magnitude E0 greater than the velocity of the acoustic wave divided by the electron mobility p. of the semiconductor,

c. means for applying a magnetic field to the semiconductor transverse to said drift field and parallel to the cross product of the outward directed normal vector to the semiconductor surface adjacent to said piezoelectric and said electric field, in said order,

. the product of the magnitude of the magnetic field and the semiconductor mobility being much greater that unity,

e. the thickness of the semiconductor is substantially greater than the relaxation frequency w a divided by the electron drift velocity v, and is also substantially greater than the Debye wavelength A of the electron in the semiconductor.

2. An apparatus for amplifying an acoustic wave on the surface of the piezoelectric crystal as recited in claim 1 wherein the semiconductor is located adjacent and parallel to the piezoelectric surface within a distance less than the wavelength of the acoustic wave to be amplified.

3. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the semiconductor is located as close as possible, but not touching, said piezoelectric.

4. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the depletion depth of said semiconductor is less than a wavelength of the acoustic wave to be amplified.

5. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the depletion depth of said semiconductor is a minimum distance and substantially less than the wavelength of the acoustic wave to be amplified.

6. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 

1. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal comprising: a. a semiconductor located immediately adjacent to and with a surface substantially parallel to said piezoelectric surface, b. means for applying a drift field across and parallel to the surface of said semiconductor adjacent to said piezoelectric, with a direction opposing the direction of propagation of said acoustic wave and of magnitude EO greater than the velocity of the acoustic wave divided by the electron mobility Mu of the semiconductor, c. means for applying a magnetic field to the semiconductor transverse to said drift field and parallel to the cross product of the outward directed normal vector to the semiconductor surface adjacent to said piezoelectric and said electric field, in said order, d. the product of the magnitude of the magnetic field and the semiconductor mobility being much greater that unity, e. the thickness of the semiconductor is substantially greater than the relaxation frequency omega divided by the electron drift velocity vo and is also substantially greater than the Debye wavelength lambda D of the electron in the semiconductor.
 2. An apparatus for amplifying an acoustic wave on the surface of the piezoelectric crystal as recited in claim 1 wherein the semiconductor is located adjacent and parallel to the piezoelectric surface within a distance less than the wavelength of the acoustic wave to be amplified.
 3. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the semiconductor is located as close as possible, but not touching, said piezoelectric.
 4. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the depletion depth of said semiconductor is less than a wavelength of the acoustic wave to be amplified.
 5. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein the depletion depth of said semiconductor is a minimum distance and substantially less than the wavelength of the acoustic wave to be amplified.
 6. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 further comprising means for applying an electrical voltage across the piezoelectric and semiconductor whereby an electric field is induced across the depletion region of the semiconductor effectively decreasing the depletion depth.
 7. An apparatus for amplifying an acoustic wave on the surface of a piezoelectric crystal as recited in claim 1 wherein omega va2/ omega pvo2 << 1 and omega is the relaxation frequency, va is the velocity of the acoustic wave, vo is the velocity of the drift electrons and omega D is the diffusion frequency. 